We then show convergence of these generalized gradient structures under a mean-field scaling and the large-population limit in the sense of Energy Dissipation Principles (EDPs) (see [1]}). The limiting gradient flow is the Liouville equation corresponding to the mean-field equation, namely a transport equation that describes the evolution of the law of a process that follows deterministic dynamics described by (REF ) but for possibly random initial conditions. This connection between the Liouville equation and the mean-field equation is made rigorous with the help of a modification of the superposition principle of [2]}.
